Risa, Joelle and Gem each had some balls and decided to play a game with their balls. In round 1, Risa lost ¹₂ of her balls to Joelle. In round 2, Joelle lost ¹₂ of her total number of balls to Gem. In round 3, Gem lost ¹₂ of her total number of balls to Risa. In the end, Risa, Joelle and Gem had 124, 88 and 53 balls respectively. How many balls did Joelle have at first?

	Risa	Joelle	Gem
Before  1	2 b	105
Change 1	- 1 b	+ 1 b
After 1	1 b	176
Before 2	71	2 u
Change 2		- 1 u	+1
After 2		1 u	106
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Risa, Joelle and Gem in the end	124	88	53

Working backwards.

1 p = 53

At the start of Round 3:
Number of balls that Gem had
= 2 p
= 2 x 53 
= 106

At the start of Round 2:
Number of balls that Risa had
= 124 - 1 p
= 124 - 53
= 71

At the end of Round 3:
Number of balls that Joelle had = 88

1 u = 88

At the end of Round 1:
Number of balls that Joelle had
= 2 u
= 2 x 88 
= 176

1 b = 71 

At the end of Round 1:
Number of balls that Risa had = 71

At the start of Round 1:
Number of balls that Joelle had
= 176 - 1 b
= 176 - 71
= 105

Answer(s): 105